| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Solving linear systems using matrices |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question testing basic matrix operations: extracting equations from matrix form, finding a 2×2 inverse using the standard formula, and multiplying to solve. While it's Further Maths content, the mechanical nature and standard textbook format make it slightly easier than average overall, though harder than typical Core questions on the same techniques. |
| Spec | 4.03a Matrix language: terminology and notation4.03n Inverse 2x2 matrix4.03r Solve simultaneous equations: using inverse matrix |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(2x - 5y = 9\) | B1 | |
| \(3x + 7y = -1\) | B1 [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(M^{-1} = \frac{1}{29}\begin{pmatrix} 7 & 5 \\ -3 & 2 \end{pmatrix}\) | M1, A1 [2] | Divide by determinant; c.a.o. |
| \(\frac{1}{29}\begin{pmatrix} 7 & 5 \\ -3 & 2 \end{pmatrix}\begin{pmatrix} 9 \\ -1 \end{pmatrix} = \frac{1}{29}\begin{pmatrix} 58 \\ -29 \end{pmatrix}\) | M1, A1(ft) [2] | Pre-multiply by their inverse; for both |
| \(\Rightarrow x = 2, y = -1\) |
# Question 2(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $2x - 5y = 9$ | B1 | |
| $3x + 7y = -1$ | B1 **[2]** | |
---
# Question 2(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| $M^{-1} = \frac{1}{29}\begin{pmatrix} 7 & 5 \\ -3 & 2 \end{pmatrix}$ | M1, A1 **[2]** | Divide by determinant; c.a.o. |
| $\frac{1}{29}\begin{pmatrix} 7 & 5 \\ -3 & 2 \end{pmatrix}\begin{pmatrix} 9 \\ -1 \end{pmatrix} = \frac{1}{29}\begin{pmatrix} 58 \\ -29 \end{pmatrix}$ | M1, A1(ft) **[2]** | Pre-multiply by their inverse; for both |
| $\Rightarrow x = 2, y = -1$ | | |
---2 You are given that $\mathbf { M } = \left( \begin{array} { r r } 2 & - 5 \\ 3 & 7 \end{array} \right)$.\\
$\mathbf { M } \binom { x } { y } = \binom { 9 } { - 1 }$ represents two simultaneous equations.\\
(i) Write down these two equations.\\
(ii) Find $\mathbf { M } ^ { - 1 }$ and use it to solve the equations.
\hfill \mbox{\textit{OCR MEI FP1 2010 Q2 [6]}}